Since \(\rho (M_n)=0\)  for all \(n\in \mathbb {N}\)  we obtain that
\(\lbrace M_n: n\in \mathbb {N}\rbrace \subset S\)  and that follows i.e. that result of Weisz [1]} (see also [2]}) that restricted maximal operator (REF ) is bounded from the Hardy space \(H_{p}\)  to the space \(L_{p}.\)
